TY - JOUR
ID - 37336
TI - On Preserving Properties of Linear Maps on $C^{*}$-algebras
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Golfarshchi, Fatemeh
AU - Khalilzadeh, Ali Asghar
AD - Department of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.
AD - Department of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.
Y1 - 2020
PY - 2020
VL - 17
IS - 1
SP - 125
EP - 137
KW - Absolute value preserving
KW - $*$-homomorphism
KW - Unitary preserving
KW - numerical range
DO - 10.22130/scma.2019.107553.607
N2 - Let $A$ and $B$ be two unital $C^{*}$-algebras and $\varphi:A \rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $\varphi$ is unital, $B$ is commutative and $V(\varphi(a)^{*}\varphi(b))\subseteq V(a^{*}b)$ for all $a,b\in A$, then $\varphi$ is a $*$-homomorphism. It is also shown that if $\varphi(|ab|)=|\varphi(a)\varphi(b)|$ for all $a,b\in A$, then $\varphi$ is a unital $*$-homomorphism.
UR - https://scma.maragheh.ac.ir/article_37336.html
L1 - https://scma.maragheh.ac.ir/article_37336_5e75596460a797fec56dbf1fd1ff1242.pdf
ER -